=Paper=
{{Paper
|id=Vol-2803/paper15
|storemode=property
|title=Modeling the operation of a distributed high-load monitoring
system for a data transmission network in a non-stationary
mode
|pdfUrl=https://ceur-ws.org/Vol-2803/paper15.pdf
|volume=Vol-2803
|authors=Kirill Shardakov,Vladimir Bubnov,Svetlana Kornienko
}}
==Modeling the operation of a distributed high-load monitoring
system for a data transmission network in a non-stationary
mode==
https://ceur-ws.org/Vol-2803/paper15.pdf
Modeling the operation of a distributed high-load monitoring
system for a data transmission network in a non-stationary
mode
Kirill Shardakova, Vladimir Bubnova and Svetlana Kornienkoa
a
Emperor Alexander I St. Petersburg State Transport University, Moskovskiy avenue, 9, Saint-Petersburg,
190031, Russian Federation
Abstract
The article discusses the numerical-analytical and simulation models of a high-load
monitoring system. The examples of modeling are presented and the technical problem of
choosing the hardware configuration of the simulated monitoring system is solved, which
makes it possible to reduce the time spent by the task in the system by more than 2 times.
Keywords
Non-stationary queuing system, monitoring system, modeling, simulation model, numerical-
analytical model
monitoring system under various loads. The
1. Introduction proposed model uses an improved recursive
algorithm for generating a list of system states
and a matrix of coefficients of an ODE system
Automated monitoring systems are an
without constructing a graph of states and
important part of any information system.
transitions of the non-stationary queueing
Monitoring is a continuous process of
system and deriving the general equation of
observing and registering object parameters,
the ODE system as in [10-13]. On the basis of
processing them, and comparing them with
a parallel-serial model, numerical-analytical
threshold values. This monitoring system must
[14] and simulation [15] models of a
cope with the increasing workload. Zabbix is
distributed high-load monitoring system for a
the most popular and easily scalable for load
data transmission network were developed and
adaptation free monitoring system for
implemented.
information systems [1].1
Most often, the authors consider the
stationary mode of operation of such systems 2. Brief description of the
in the context of queuing systems, however, it simulated monitoring system
is the non-stationary mode of operation that is
of greatest interest. The current state of the As it already known, the monitoring system
issue of non-stationary queuing systems is under consideration allows you to distribute
considered in more detail in [2]. The beginning the load and scale it through the use of proxy
of the “nonstationary” queueing theory was servers. Each proxy server collects data from a
laid in [3–5] and continued in [6–7]. separate set of devices, and then sends the data
In [8-9], a model is proposed that allows to the main server that processes it.
one to simulate the behavior of such a Figure 1 shows a general diagram of the
interaction of system components. Such a
1 Models and Methods for Researching Information Systems
system can also be considered as a queuing
in Transport, Dec. 11-12, St. Petersburg, Russia system. The queuing system representation is
EMAIL: k.shardakov@gmail.com (K.S. Shardakov); shown in Figure 2.
bubnov1950@yandex.ru (V.P. Bubnov); sv.diass99@yandex.ru
(S.V. Kornienko);
ORCID: 0000-0002-6742-3011 (V.P.Bubnov); ORCID: 0000-
0003-2683-0697 (S.V. Kornienko)
©️ 2020 Copyright for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
107
Figure 1: Simplified diagram of the interactions of the monitoring system components
Figure 2: Simplified diagram of the parallel-serial non-stationary queueing system
The arrival intensity of tasks higher than
3. Numerical-analytical modeling the service rates allows one to simulate the
non-stationary operation of the system.
of work in a non-stationary As a result of the simulation, it was found
mode that the model with such initial data generates
1001 possible states of the system. This leads
Numerical and analytical modeling was to the need to compose and solve the system of
carried out using the software package [14]. Chapman-Kolmogorov differential equations
The result of the operation of such a model is with the same number of equations for
the calculated probabilities of all possible calculating the probabilities of the states of the
states of the system at given time moments. system at given time moments.
Consider a model with the following initial As you can see from Figure 3, after time
inputs: moment 5, the probability of the onset of the
1. Amount of proxy servers – 2; absorbing state begins to increase sharply and
2. Amount of incoming tasks – 10; by time moment 18 is practically equal to 1.
3. Amount of calculated time moments, The obtained simulation results allow us to
starting from zero – 30; build graphs of the probability distribution of
4. Intensity of tasks arriving – 3; the states of the simulated system at each time
5. Intensity of processing tasks for proxy moment, which allows us to consider in more
– 1; detail the probability distribution at the turning
6. Intensity of processing tasks for main points in time, which are clearly expressed in
server – 2. Figure 3. Figure 4 shows the probability
108
distribution at time moment 0, as we can see, probabilities, which indicate that new requests
this is the initial state of the system and its can arrive in the system with the least
probability is equal to one, while the probability, and those that have already arrived
probabilities of other states are equal to zero. will be processed with a higher probability.
As can be seen from Figure 5, the Figure 6 allows us to say that at time
probability distribution of states at time moment 18 the absorbing state has the highest
moment 5 allows us to say that at this time probability, while the probability of the system
moment the final states have the highest being in other states is negligible.
Figure 3: Absorbing state, 2 proxy servers, 10 tasks
Figure 4: Time moment 0, 2 proxy servers, 10 tasks
109
Figure 5: Time moment 5, 2 proxy servers, 10 tasks
Figure 6: Time moment 18, 2 proxy servers, 10 tasks
With an increase in the number of proxy shifted from 18 to 16, which, as expected,
servers from 2 to 3, in Figure 7 we can see that indicates a slightly higher throughput of such a
the time moment with the maximum system compared to the system in which there
probability of the onset of the absorbing state are 2 proxies.
110
Figure 7: Absorbing state, 3 proxy servers, 10 tasks
So, the numerical-analytical model makes 4. Intensity of processing tasks for proxy
it possible to determine the probabilistic – 1;
characteristics of the system, as well as to 5. Intensity of processing tasks for main
consider their changes dynamically at different server – 2.
time moments. The arrival intensity of tasks higher than
the service rates allows one to simulate the
non-stationary operation of the system.
4. Simulation modeling The path of such a model through the state
graph was 3001 states. Figure 8 shows the
number of tasks in queues to proxy servers and
Simulation modeling was carried out using
to the main server, as well as the number of
the software package [15]. The result of this
tasks they have already served. Values are
model is the following statistical data for each
listed for each condition passed by the system.
application:
As we can see, the queue to proxy servers is
1. Time in the queue to the proxy server;
constantly increasing until all requests has
2. Service time on the proxy server;
arrive to the system, after which the queue to
3. Time in the queue to the main server;
proxy begins to decreasing rapidly. At the
4. Service time on the main server;
same time, the queue to the main server and
5. The total time spent by the task in the
the gap in the number of requests served by
system.
proxy servers and the main server is minimal.
Additionally, the model allows tracing the
In Figure 9, we can see that the residence
full path through the system state graph.
time of each new request in the system
Consider a model with the following initial
increases up to 200 conventional units of time,
inputs:
which is obviously due to the low throughput
1. Amount of proxy servers – 2;
of proxy servers.
2. Amount of incoming tasks – 1000;
3. Intensity of tasks arriving – 3;
111
Figure 8: Queue size, 2 proxies, 1000 tasks
Figure 9: Time, 2 proxies, 1000 tasks
To fix the problem, let's simulate an task in the system is still close to 200. From
increase in proxy servers up to 3 with the this we can conclude that the growth of the
remaining parameters unchanged. As you can queue to the proxy in this configuration is
see from Figure 10, now the queue to the insignificant, but it is impossible to reduce
proxy is accumulating much less intensively, their number or performance, since this will
however, the queue to the main server reduce the queue to the main server, but
continues to accumulate even after all requests increase the queue to the proxy. Thus, the
have arrived to the system. changes are leveled and the total time spent by
At the same time, from Figure 11, we can the order in the system will not change.
notice that the maximum total time spent by an
112
Figure 10: Queue size, 3 proxies, 1000 tasks
Figure 11: Time, 3 proxies, 1000 tasks
From Figure 13, we can see that the time in
Let's simulate the behavior of the system the queue to the proxy and to the main server
once again with an increase in the intensity of is approximately the same, and the maximum
processing requests on the main server to 2.5. time for a request to be in the system is about
As it can be seen from Figure 12, queues 80 conventional units of time, which is more
accumulate almost evenly and are small. than 2 times less than the values obtained in
the simulation with the initial conditions.
113
Figure 12: Queue size, 3 proxies, 1000 tasks, 2.5 main server intensity
Figure 13: Time, 3 proxies, 1000 tasks, 2.5 main server intensity
So, the simulation model allows solving the 5. Conclusion
technical problem of determining the
minimum required hardware configuration of
The article discusses the numerical-
the system to service a finite number of tasks
analytical and simulation models of the
with a certain level of service - the time the
operation of a high-load distributed monitoring
task is in the system.
system for a data transmission network in a
non-stationary mode. These models make it
possible to determine the probabilistic
characteristics of the system's behavior, as
114
well as to determine the necessary hardware vol. 76, no. 2, pp. 285–288 (in
configuration to maintain the required service Russian).
level of tasks. [7] B. Conolly Generalized State
Further development of the topic can be Dependent Eriangian Queues
adding priorities to requests and adding the (speculation about calculating easure
transfer of packages of requests from the of effectiveness). Applied Probability,
proxy to the main server. 1975, no. 2. рр. 358–363.
[8] K. Shardakov, V. Bubnov, Stochastic
Research support. Research carried out on this Model Of A High-Loaded Monitoring
topic was carried out within the framework of System Of Data Transmission
the budget topic No. 0073–2019–0004 Network // Proceedings of Models and
Methods of Information Systems
Research Workshop. 2019. P. 29–34.
References [9] K. Shardakov, V. Bubnov, Non-
stationary parallel-serial model of a
high-load monitoring system.
[1] K. Shardakov, Comparative analysis
Information and space, 2020(3), pp.
of the popular monitoring systems for
56-67 (2020). (in Russian)
network equipment distributed under
[10] V. Bubnov, V. Safonov, V.
the GPL license. Intellectual
Smagin About the loading of a
Technologies on Transport 2018(1),
computing system with a varying
pp. 44–48 (2018). (in Russian)
intensity of receipt of tasks, Automatic
[2] V. Bubnov, V. Safonov, K.
Control and Computer Sciences, 1987,
Shardakov, Overview of existing
no. 6, pp. 19–22 (in Russian).
models of non-stationary queuing
[11] V. Bubnov, V. Safonov
systems and methods for their
Development of dynamic models of
calculation. Systems of Control,
non-stationary queuing systems. Saint-
Communication and Security, 2020,
Petersburg, 1999. 64 p. (in Russian).
no. 3, pp. 65–121 (in Russian). DOI:
[12] V. Bubnov A. Khomonenko, A. Tyrva
10.24411/2410-9916-2020-10303
Software reliability model with coxian
[3] I. Kovalenko About the queuing
distribution of length of intervals
system with the speed of service,
between errors detection and fixing
depending on the number of
moments // International Computer
requirements in the system, and
Software and Applications
periodic shutdown of channels.
Conference. 2011. pp. 310-314.
Problems of Information
[13] V. Bubnov, A. Tyrva, A. Khomonenko
Transmission, 1971, vol. 7, no. 2, pp.
Model of reliability of the software
108–114 (in Russian).
with coxian distribution of length of
[4] I. Ezhov, M. Korneichuk, I. Oliinyk D.
intervals between the moments of
Distribution of the number of repair
detection of errors // International
system channels when the flow rate
Computer Software and Applications
changes in a special way. Kibernetika,
Conference. 34th Annual IEEE
1976, no. 3, pp. 92–97 (in Russian).
International Computer Software and
[5] L. M. Abol'nikov Non-stationary
Applications Conference, COMPSAC
queuing problem for systems with an
2010. 2010. pp. 238-243
infinite number of channels with
[14] K. Shardakov, V. Bubnov The
group receipt of requirements.
program for the numerical-analytical
Problems of Information
calculation of the state probabilities of
Transmission, 1968, vol. 4, no. 3, pp.
a non-stationary acyclic queueing
99-102 (in Russian).
network with a finite number of tasks.
[6] G. Arsenishvili Singleline queuing
The Certificate on Official
system with queue-dependent
Registration of the Computer Program.
incoming flow rate. Soobshcheniia
No. 2020662856, 2020.
Akademii nauk Gruzinskoi SSR, 1974,
[15] K. Shardakov, V. Bubnov The
program for simulating the process of
115
queueing tasks in a non-stationary
acyclic queueing network with a finite
number of tasks. The Certificate on
Official Registration of the Computer
Program. No. 2020663070, 2020.
116